This whitepaper contains great insights on each. In a nutshell:
Artificial Intelligence (AI) is a “a huge set of tools for making computers behave intelligently” and in an automated fashion. This includes voice assistants, recommendation systems, and self-driving cars.
Machine Learning (ML) is the “field of study that gives computers the ability to learn without being explicitly programed.” The lion’s share of ML involves computers learning patterns from existing data and applying it to new data in the form of making predictions, such as predicting whether an email is spam or not, whether a customer will churn or not, and diagnosing a particular piece of medical imaging.
Data Science (DS) is about making discoveries and creating insights from data and communicating these insights and discoveries to non-technical stakeholders.